A registered nurse is trying to develop a diet plan for patients. The required nutritional elements are the total daily requirements of each nutritional element as indicated in Table 2:
Required nutritional element total and daily requirements
|
Calories
|
Not more than 2,700 calories
|
|
Carbohydrates
|
Not more than 300 grams
|
|
Protein
|
Not less than 250 grams
|
|
Vitamins
|
Not less than 60 units
|
The nurse has four basic types to use when planning the menus. The units of nutritional element per unit of food type are shown in Table 3 below. Note that the cost associated with a unit of ingredient also appears at the bottom of Table 3.
Required nutritional element and units of nutritional elements per unit of food type
|
Element
|
Milk
|
Chicken
|
Bread
|
Vegetables
|
|
Calories
|
160
|
210
|
120
|
150
|
|
Carbohydrates
|
110
|
130
|
110
|
120
|
|
Protein
|
90
|
190
|
90
|
130
|
|
Vitamins
|
50
|
50
|
75
|
70
|
|
Cost per unit
|
£0.42
|
£0.68
|
£0.32
|
£0.17
|
Moreover, due to dietary restrictions, the following aspects should also be considered when developing the diet plan:
- The chicken food type should contribute at most 25% of the total caloric intake that will result from the diet plan.
- The vegetable food type should provide at least 30% of the minimum daily requirements for vitamins.
Complete the following:
Provide a linear programming formulation for the above case. (You do not need to solve the problem.